Update on this thread: I was finally able to get all four wheels on the car. Here's what I ended up doing:
1. Removed stock front drum break setup and installed a Wilwood disc break kit (https://www.opgi.com/riviera/1963/brake-systems/disc-brakes/BR03001/)
2. Had a machine shop mill a chamfer on the end of the rotors to fit inside the center bore of the wheels—the end of the hub on the rotor was hitting the outside end of the center bore of the wheel.
3. Also had the machine shop enlarge the center bore on all four wheels slightly. That way they fit perfectly around the hub of the front discs and on the stock rear drums.
I'm pleased with the ways the wheels fit. No spacers needed. No funny mill work that will keep me from being able to rotate the tires front to back. And best of all, it rides great and stops much better.
Next up I plan to rebuild the front end and install 1" lowering springs on all four corners.

Hi @Grapeman,
Are you running the spacers so your new wheels will clear the stock hubs? I bought an aftermarket set of wheels but they won't fit around the hubs on my 1963 Riviera. Did you need to install longer studs to make your wheels fit properly with the spacers?
Thank you,
Patrick

Hello @Jim Cannon,
Thanks for your interest in my car and your willingness to help decode its history. I have a few photos of the car, but not many detail shots. If you'll let me know what I should photograph, I'll shoot and upload photos of those details so you can get a closer look.
The car is in pretty rough shape aesthetically, but mechanically it is very sound. I drive it pretty regularly and plan to restore it to near factory condition in the coming years. Any guidance you can provide on what definitely needs to be preserved would be much appreciated.
It is pretty exciting to think that this car rolled off the line so early in 1963.
Thanks,
Patrick Turner

Thanks for all the input. I had an inkling that this car was fairly early off the line, but wasn't sure how to verify that. The VIN on this car is 7J1001104 which would seem to jive with the low body tag number.
This car also has power vent windows which is an option I've not seem on many 1963 Rivieras. My exposure to this year/model might be more limited than yours, Ed and Tom.

I'm trying to verify the serial number on my 1963 Buick Riviera. I thought that I had determined it based on this plate located on the firewall, but now I'm second guessing that. Is this the right place to find the serial number, or should I be looking somewhere else?

Has anyone had any experience with putting a 1965 Riviera rear bumper on a 1963? I'd really like to clean up the rear of my 1963 by filling in the tail lights in the body and moving them to the bumper.

I'm sure Summit would take the wheel back, but I really like the looks of the Boss 338 wheel. Since the wheel clears the rivets on the front drums, I supposed I could just have them all machined to clear the hubs. I will probably still need a 1/8" spacer on the front to clear the steering control arm, but that shouldn't be hard to find or have made. When I finally solve this puzzle I'll post some images so you can see how everything turned out.

I picked up a pair of Mr. Gasket (http://www.summitracing.com/nv/parts/mrg-2371/overview/) 5/16 wheel spacers from Summit Racing. They fit the lug pattern and around the rivets on the front hubs, but the center bore isn't large enough to fit around the hub. Even if it did fit around the hub, it doesn't look like the lugs would be long enough to show enough thread to safely keep the lug nuts on. So, I guess I'm back to square one. I'm thinking the best approach is going to be converting the front to disc brakes and machining the back wheels to fit around the stock hubs. Any other ideas?